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Random Probability Measures on Polish Spaces

Hans Crauel



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CRC Press
05 September 2019
In this monograph the narrow topology on random probability measures on Polish spaces is investigated in a thorough and comprehensive way. As a special feature, no additional assumptions on the probability space in the background, such as completeness or a countable generated algebra, are made. One of the main results is a direct proof of the random analog of the Prohorov theorem, which is obtained without invoking an embedding of the Polish space into a compact space. Further, the narrow topology is examined and other natural topologies on random measures are compared. In addition, it is shown that the topology of convergence in law-which relates to the statistical equilibrium -and the narrow topology are incompatible. A brief section on random sets on Polish spaces provides the fundamentals of this theory. In a final section, the results are applied to random dynamical systems to obtain existence results for invariant measures on compact random sets, as well as uniformity results in the individual ergodic theorem. This clear and incisive volume is useful for graduate students and researchers in mathematical analysis and its applications.
By:   Hans Crauel
Imprint:   CRC Press
Country of Publication:   United Kingdom
Dimensions:   Height: 229mm,  Width: 152mm, 
Weight:   249g
ISBN:   9780367395995
ISBN 10:   0367395991
Pages:   144
Publication Date:   05 September 2019
Audience:   College/higher education ,  Primary
Format:   Paperback
Publisher's Status:   Active
Notations and Some Technical Results. Random Sets. Random Probability Measures and the Narrow Topology. Prohorov Theory for Random Probability Measures. Further Topologies on Random Measures. Invariant Measures and Some Ergodic theory for Random Dynamical Systems A. The Narrow Topology on Non-Random Measures B. Scattered Results. Bibliography. Index.

Crauel, Hans

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